Algebra Examples

$(7 a - 1) (x^{2} + 2 x - 5)$

Step 1

Expand $(7 a - 1) (x^{2} + 2 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$7 a x^{2} + 7 a (2 x) + 7 a \cdot - 5 - 1 x^{2} - 1 (2 x) - 1 \cdot - 5$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$7 a x^{2} + 7 \cdot 2 a x + 7 a \cdot - 5 - 1 x^{2} - 1 (2 x) - 1 \cdot - 5$

Step 2.1.2

Multiply $7$ by $2$ .

$7 a x^{2} + 14 a x + 7 a \cdot - 5 - 1 x^{2} - 1 (2 x) - 1 \cdot - 5$

Step 2.1.3

Multiply $- 5$ by $7$ .

$7 a x^{2} + 14 a x - 35 a - 1 x^{2} - 1 (2 x) - 1 \cdot - 5$

Step 2.1.4

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$7 a x^{2} + 14 a x - 35 a - x^{2} - 1 (2 x) - 1 \cdot - 5$

Step 2.1.5

Multiply $2$ by $- 1$ .

$7 a x^{2} + 14 a x - 35 a - x^{2} - 2 x - 1 \cdot - 5$

Step 2.1.6

Multiply $- 1$ by $- 5$ .

$7 a x^{2} + 14 a x - 35 a - x^{2} - 2 x + 5$

Step 2.2

Move $- 35 a$ .

$7 a x^{2} + 14 a x - x^{2} - 35 a - 2 x + 5$